One setting that is commonly used to explore the spatial degrees of freedom of light is that of FWM induced by amplified spontaneous emission in a hot atomic vapor, with a 3-level cascade system [1]}, [2]}, [3]}, [4]}, [5]}.
In cold atomic samples, FWM was employed to transfer OAM from incident to generated beams in nondegenerate [6]} and degenerate [7]} atomic systems, to transfer more complicated phase structures (obtained by superimposing LG modes of different orders) [8]}, and to store the information carried by the spatial structure of light in the ensemble of atoms, and later retrieve it [9]}, [10]}.
